[mlyle]

We obviously have a huge variation in spread. Indeed, the choir is evidence of superspreaders who produce many cases, and we have an average R0 of 2-3. Singing loudly in enclosed spaces with many people is an example of a contact network structure that causes greatly increased susceptibility and contagion. Indeed, it proves the whole point!

But, the belief that herd immunity = 1 - (1 / R) is based on the assumption that those infected have equal susceptibility and equal probability of spread. This is a fair assumption when it comes to a vaccination program which will administer doses not correlated to susceptibility and contact network structure. It is not a fair assumption when it comes to actual spread of disease in the wild, which will preferentially spread in the more susceptible networks.

Reality is certainly better than this; the question is how much better. There's been some quality analysis of time-series data that implies the threshold may be 20-30%.

I believe that New York City's quick decline in death rates compared to jurisdictions with similar or stricter controls but lower seropositivity may imply that ~20% exposure is enough to significantly attenuate spread.

[acqq]

> There's been some quality analysis of time-series data that implies the threshold may be 20-30%.

Please provide the sources. I however don't expect it can be that good, and I'm quite sure it will be proven that it's impossible to expect for the epidemics to stop once 20 or 30% of the population is infected, if that is your claim. If your claim is that once that "threshold" is reached the speed of the spread changes, well that speed changed already much earlier: most people just don't have any motive to sacrifice for the "economy" or the rich or whatever. You don't need the laws for the people to figure out that much.

[mlyle]

This is a good introductory treatment of the topic:

https://www.medrxiv.org/content/10.1101/2020.04.27.20081893v...

> well that speed changed already much earlier

Your comment is a bit self-contradictory and muddled. That is, we're talking about the herd immunity threshold under baseline behavior; what percentage of the population needs to have been infected to result in infections decaying with original behaviors.

The point I was making is that it seems like case counts are decaying much quicker in regions with high seropositivity than other regions with similar regulations and similar empirical measures of mobility. This would imply that under current conditions even the modest immunity reached seems to make a bigger difference than naive assumptions about immunity and resulting Rt imply.

We already know that contact networks are not uniform (source: duh); further, individual susceptibility apparently varies significantly (from genetic studies). These factors significantly change the percentage that must be organically infected to reach herd immunity.

It's worth noting that this difference has both optimistic and pessimistic implications. Optimistic: regions that have high seropositivity are more likely to have the worst behind them. Pessimistic: the amount of vaccination to have equal effect probably far out-strips current seropositivity rates, because it can't effectively be targeted based upon susceptibility and network structure.

[acqq]

I tried but I don’t see that the paper proved anything about the current pandemics?

[mlyle]

A paper doesn't "prove" anything, but it does utilize and cite upon real world mobility data and real world susceptibility and transmissibility data for many diseases, including early estimates of these for SARS-CoV-2, e.g. https://wellcomeopenresearch.org/articles/5-67 is cited and used in the estimate of the coefficient of variation.

There was very little data on overdispersion and differential susceptibility for SARS-CoV-2 at the time that paper was written, but there was some. What existed at the time was in line with the better estimates from SARS-CoV-1, etc, that the paper also used. Further evidence has emerged since, both of variable susceptibility and exposure and of actual mechanisms of variable susceptibility-- some surprising like https://www.medrxiv.org/content/10.1101/2020.04.08.20058073v...

[acqq]

Good, so we agree that nobody has proved for SARS-CoV-2 that less than 70% of can be infected to achieve the so-called "herd immunity" (even when knowing that different people allow some very lax definitions of "herd immunity").

[mlyle]

Yes, and nobody has proven really -anything- about most things, by this metric. All we have is evidence of varying quality.

But, again: it's pretty much settled science that Rt = 1 when 1-(1/R0) is infected is a worst case not very often attained, and the evidence so far with COVID-19 (looking at time series data, evidence of non-uniform susceptibility, clear evidence of non-uniform contact networks, significant evidence of overdispersion, etc) leans strongly that way.

Bigger issue is: if 25% infected yields expected Rt of under 1 (the threshold for herd immunity, and I think this is likely)... you'll still have a fair number of cases, because people will come from other jurisdictions with the disease and it'll trigger chains of spread that only slowly decay / peter out each time. If you're one of the other 75%, you're hardly safe, because you can be exposed to one of these chains. Only vaccination can address this, and it's not even a complete fix.